(b)
Figure 4. Relationship between interaction energy and the geometrical parameters in R-Ph-CN…PO2F complexes, including (a) the N…P intermolecular distance r(N…P), and (b) the dihedral angle F-P-O-O.

3.1.3 AIM and NBO analyses

The quantum theory of AIM[52] is useful to analyze various intermolecular interactions. The N…P pnicogen bond is characterized by the existence of an intermolecular BCP between N atom of R-Ph-CN and the P atom of PO2F. Values of the corresponding topological parameters are gathered in Table 3. The Laplacian ∇2ρ of the BCPs are all positive, and this indicates a depletion of the electron density, which is common in closed-shell kind of interactions in the complexes[53]. It is known that the signs of ∇2ρBCP and HBCP can be used to characterize the strength of intermolecular interaction and describe the covalent properties of a bond [54]. In the complexes studied herein, the positive ∇2ρBCP and negative HBCP at the P…N BCP in all cases indicate that the P…N pnicogen bonding can be classified as medium strength interaction with partially covalent characteristics[55]. It is observed from Table 3 that the value of HBCP become more negative, as the interaction energy of R-Ph-CN…PO2F increases, indicating the more covalent character in the P…N interactions. As seen in Figure 5, there is a good linear relationship between binding distance r(N…P) and bond critical point electron density (ρN…P). Therefore, it is accepted that the electron density at the BCPs is a good measurement to estimate the strength of the pnicogen bond of the complexes we studied. Similar results have been observed in some H-bonded complexes, but it is the logarithm of the electron density that participated in the linear relationship[56].
Table 3. The AIM topological parameters at the N…P BCPs and the natural bond orbital analysis of the R-Ph-CN…PO2F binary complexes.